Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
26901	Evaluate the Integral	integral from 0 to 1 of (1-x)^9 with respect to x	$\int_{0}^{1} {(1 - x)}^{9} d x$
26902	Evaluate the Integral	integral from 0 to 1 of (8y^2-y+1)^(-1/3)(32y-2) with respect to y	$\int_{0}^{1} {(8 y^{2} - y + 1)}^{- \frac{1}{3}} (32 y - 2) d y$
26903	Evaluate the Integral	integral from 0 to 1 of (6t)/(t^2+1) with respect to t	$\int_{0}^{1} \frac{6 t}{t^{2} + 1} d t$
26904	Evaluate the Integral	integral from 0 to 1 of (3x-2)^2 with respect to x	$\int_{0}^{1} {(3 x - 2)}^{2} d x$
26905	Evaluate the Integral	integral from 0 to 1 of ax+bx^2 with respect to x	$\int_{0}^{1} a x + b x^{2} d x$
26906	Evaluate the Integral	integral from 0 to 1 of 7x^2-4x+9 with respect to x	$\int_{0}^{1} 7 x^{2} - 4 x + 9 d x$
26907	Find dy/dx	8x^2+xy+8y^2=17	$8 x^{2} + x y + 8 y^{2} = 17$
26908	Evaluate the Integral	integral of 1.75+0.16x-0.0015x^2 with respect to x	$\int 1.75 + 0.16 x - 0.0015 x^{2} d x$
26909	Evaluate the Integral	integral from 0 to 1 of (2t)/(1+t^2) with respect to t	$\int_{0}^{1} \frac{2 t}{1 + t^{2}} d t$
26910	Evaluate the Integral	integral from 0 to 1 of 1/(1-x^2) with respect to x	$\int_{0}^{1} \frac{1}{1 - x^{2}} d x$
26911	Evaluate the Integral	integral from 0 to 1 of 1/(4x+1) with respect to x	$\int_{0}^{1} \frac{1}{4 x + 1} d x$
26912	Evaluate the Integral	integral from 0 to 1 of (e^(5x))/(e^(3x)) with respect to u	$\int_{0}^{1} \frac{e^{5 x}}{e^{3 x}} d u$
26913	Evaluate the Integral	integral from 0 to 1 of square root of t^4+7t(4t^3+7) with respect to t	$\int_{0}^{1} \sqrt{t^{4} + 7 t} (4 t^{3} + 7) d t$
26914	Evaluate the Integral	integral from 0 to 1 of tan(pi/4y)^2 with respect to y	$\int_{0}^{1} \tan^{2} (\frac{π}{4} y) d y$
26915	Evaluate the Integral	integral from 0 to 1 of e^(arctan(x)) with respect to x	$\int_{0}^{1} e^{\arctan (x)} d x$
26916	Evaluate the Integral	integral from 0 to 1 of (sin(x))/x with respect to x	$\int_{0}^{1} \frac{\sin (x)}{x} d x$
26917	Evaluate the Integral	integral from 0 to 1 of ( natural log of x)/( square root of x) with respect to x	$\int_{0}^{1} \frac{\ln (x)}{\sqrt{x}} d x$
26918	Evaluate the Integral	integral from 0 to 1 of e^x-2 with respect to x	$\int_{0}^{1} e^{x} - 2 d x$
26919	Find dy/dx	ycos(x)=5x^2+3y^2	$y \cos (x) = 5 x^{2} + 3 y^{2}$
26920	Evaluate the Integral	integral from 0 to 1 of x^2ydx with respect to x	$\int_{0}^{1} x^{2} yds x d x$
26921	Evaluate the Integral	integral from 0 to 1 of x^7 square root of 1-x^8 with respect to x	$\int_{0}^{1} x^{7} \sqrt{1 - x^{8}} d x$
26922	Evaluate the Integral	integral from 0 to 1 of x/(x+1) with respect to x	$\int_{0}^{1} \frac{x}{x + 1} d x$
26923	Evaluate the Integral	integral from -pi to pi of sin(x) with respect to x	$\int_{- π}^{π} \sin (x) d x$
26924	Evaluate the Integral	integral from 0 to 1 of x^19+19^x with respect to x	$\int_{0}^{1} x^{19} + 19^{x} d x$
26925	Evaluate the Integral	integral from 0 to 1 of 3+1/4u^4-2/3u^9 with respect to u	$\int_{0}^{1} 3 + \frac{1}{4} u^{4} - \frac{2}{3} u^{9} d u$
26926	Find dy/dx	xy+x^3=y^2	$x y + x^{3} = y^{2}$
26927	Evaluate the Integral	integral from 0 to 0 of 3x-3 with respect to x	$\int_{0}^{0} 3 x - 3 d x$
26928	Evaluate the Integral	integral from 0 to 0.3 of 2e^(-x^2) with respect to x	$\int_{0}^{0.3} 2 e^{- x^{2}} d x$
26929	Evaluate the Integral	integral from 0 to -x^2-y^2 of x with respect to z	$\int_{0}^{- x^{2} - y^{2}} x d z$
26930	Evaluate the Integral	integral from 0 to 0.5 of 3/( square root of 1-x^2) with respect to x	$\int_{0}^{0.5} \frac{3}{\sqrt{1 - x^{2}}} d x$
26931	Evaluate the Integral	integral from 0 to 0.9 of cos( square root of 6x) with respect to x	$\int_{0}^{0.9} \cos (\sqrt{6 x}) d x$
26932	Evaluate the Integral	integral from 0 to cube root of pi^2 of square root of xcos(x^(3/2))^2 with respect to x	$\int_{0}^{\sqrt[3]{π^{2}}} \sqrt{x} \cos^{2} (x^{\frac{3}{2}}) d x$
26933	Evaluate the Integral	integral from 0 to pi/6 of 6sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{6}} 6 \sec^{2} (x) d x$
26934	Evaluate the Integral	integral from 0 to pi/6 of (1-cos(3t))sin(3t) with respect to t	$\int_{0}^{\frac{π}{6}} (1 - \cos (3 t)) \sin (3 t) d t$
26935	Evaluate the Integral	integral from 0 to pi/4 of xtan(x) with respect to x	$\int_{0}^{\frac{π}{4}} x \tan (x) d x$
26936	Evaluate the Integral	integral from 0 to pi/4 of xcos(2x) with respect to x	$\int_{0}^{\frac{π}{4}} x \cos (2 x) d x$
26937	Evaluate the Integral	integral from 0 to pi/6 of cos(2x)^-5sin(2x) with respect to x	$\int_{0}^{\frac{π}{6}} \cos^{- 5} (2 x) \sin (2 x) d x$
26938	Evaluate the Integral	integral from 0 to pi/6 of cos(2x)^-6sin(2x) with respect to x	$\int_{0}^{\frac{π}{6}} \cos^{- 6} (2 x) \sin (2 x) d x$
26939	Evaluate the Integral	integral from 0 to pi/8 of (sec(2x)^2)/(3+tan(2x)) with respect to x	$\int_{0}^{\frac{π}{8}} \frac{\sec^{2} (2 x)}{3 + \tan (2 x)} d x$
26940	Evaluate the Integral	integral from 0 to pi/8 of cos(2x) with respect to x	$\int_{0}^{\frac{π}{8}} \cos (2 x) d x$
26941	Evaluate the Integral	integral from 0 to square root of 2/2 of 1/( square root of 1-r^2) with respect to rdr	$\int_{0}^{\sqrt{\frac{2}{2}}} \frac{1}{\sqrt{1 - r^{2}}} d r d r$
26942	Evaluate the Integral	integral from 0 to square root of pi/2 of sin(x^2) with respect to x	$\int_{0}^{\sqrt{\frac{π}{2}}} \sin (x^{2}) d x$
26943	Evaluate the Integral	integral from 0 to square root of 19 of 9x cube root of 8+x^2 with respect to x	$\int_{0}^{\sqrt{19}} 9 x \sqrt[3]{8 + x^{2}} d x$
26944	Evaluate the Integral	integral from 0 to pi/4 of sec(t)^2 with respect to t	$\int_{0}^{\frac{π}{4}} \sec^{2} (t) d t$
26945	Evaluate the Integral	integral from 0 to pi/4 of tan(x)^3sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{4}} \tan^{3} (x) \sec^{2} (x) d x$
26946	Evaluate the Integral	integral from 0 to pi/4 of square root of 1+cos(4x) with respect to x	$\int_{0}^{\frac{π}{4}} \sqrt{1 + \cos (4 x)} d x$
26947	Evaluate the Integral	integral from 0 to pi/4 of 2tan(x)sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{4}} 2 \tan (x) \sec^{2} (x) d x$
26948	Evaluate the Integral	integral from 0 to pi/4 of 2sin(pi-x) with respect to x	$\int_{0}^{\frac{π}{4}} 2 \sin (π - x) d x$
26949	Evaluate the Integral	integral from 0 to pi/4 of 4sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{4}} 4 \sec^{2} (x) d x$
26950	Evaluate the Integral	integral from 0 to pi/4 of 4sin(x)cos(x) with respect to x	$\int_{0}^{\frac{π}{4}} 4 \sin (x) \cos (x) d x$
26951	Evaluate the Integral	integral from 0 to pi/4 of 5sec(x)tan(x) with respect to x	$\int_{0}^{\frac{π}{4}} 5 \sec (x) \tan (x) d x$
26952	Evaluate the Integral	integral from 0 to pi/4 of 8cos(2x) with respect to x	$\int_{0}^{\frac{π}{4}} 8 \cos (2 x) d x$
26953	Evaluate the Integral	integral from 0 to pi/4 of 4cos(2x) with respect to x	$\int_{0}^{\frac{π}{4}} 4 \cos (2 x) d x$
26954	Evaluate the Integral	integral from 0 to pi/4 of 7sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{4}} 7 \sec^{2} (x) d x$
26955	Evaluate the Integral	integral from 0 to pi/4 of 9sec(t)^2 with respect to t	$\int_{0}^{\frac{π}{4}} 9 \sec^{2} (t) d t$
26956	Evaluate the Integral	integral from 0 to pi/4 of sec(x)tan(x) with respect to x	$\int_{0}^{\frac{π}{4}} \sec (x) \tan (x) d x$
26957	Evaluate the Integral	integral from 0 to pi/3 of 4sin(3x) with respect to x	$\int_{0}^{\frac{π}{3}} 4 \sin (3 x) d x$
26958	Evaluate the Integral	integral from 0 to pi/4 of cos(x) with respect to x	$\int_{0}^{\frac{π}{4}} \cos (x) d x$
26959	Evaluate the Integral	integral from 0 to pi/4 of sin(4x) with respect to x	$\int_{0}^{\frac{π}{4}} \sin (4 x) d x$
26960	Evaluate the Integral	integral from 0 to pi/4 of sin(t)+cos(t) with respect to t	$\int_{0}^{\frac{π}{4}} \sin (t) + \cos (t) d t$
26961	Evaluate the Integral	integral from 0 to pi/3 of 3sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{3}} 3 \sec^{2} (x) d x$
26962	Evaluate the Integral	integral from 0 to 4 of sin(x)^2 with respect to x	$\int_{0}^{4} \sin^{2} (x) d x$
26963	Evaluate the Integral	integral from 0 to pi/4 of cos(x)^2 with respect to x	$\int_{0}^{\frac{π}{4}} \cos^{2} (x) d x$
26964	Evaluate the Integral	integral of x cube root of x-1 with respect to x	$\int x \sqrt[3]{x - 1} d x$
26965	Evaluate the Integral	integral of x cube root of 81+x^2 with respect to x	$\int x \sqrt[3]{81 + x^{2}} d x$
26966	Evaluate the Integral	integral of x cube root of x+10 with respect to x	$\int x \sqrt[3]{x + 10} d x$
26967	Evaluate the Integral	integral of x+\|x\| with respect to x	$\int x + \| x \| d x$
26968	Evaluate the Integral	integral of x fourth root of 3x+1 with respect to x	$\int x \sqrt[4]{3 x + 1} d x$
26969	Evaluate the Integral	integral of x seventh root of 81+x^2 with respect to x	$\int x \sqrt[7]{81 + x^{2}} d x$
26970	Evaluate the Integral	integral of x square root of 3x-4 with respect to x	$\int x \sqrt{3 x - 4} d x$
26971	Evaluate the Integral	integral of x square root of 4x^2+3 with respect to x	$\int x \sqrt{4 x^{2} + 3} d x$
26972	Evaluate the Integral	integral of x square root of x+12 with respect to x	$\int x \sqrt{x + 12} d x$
26973	Evaluate the Integral	integral of x square root of 8-4x^2 with respect to x	$\int x \sqrt{8 - 4 x^{2}} d x$
26974	Evaluate the Limit	limit as x approaches pi/4 of (1-tan(x))/(sin(x)-cos(x))	$lim_{x \to \frac{π}{4}} \frac{1 - \tan (x)}{\sin (x) - \cos (x)}$
26975	Evaluate the Integral	integral of x log base 5 of x with respect to x	$\int x \log_{5} (x) d x$
26976	Evaluate the Integral	integral of x square root of 10-x^2 with respect to x	$\int x \sqrt{10 - x^{2}} d x$
26977	Evaluate the Integral	integral of x square root of 11-x^2 with respect to x	$\int x \sqrt{11 - x^{2}} d x$
26978	Evaluate the Limit	limit as t approaches 5 of (s(t)-s*5)/(t-5)	$lim_{t \to 5} \frac{s (t) - s \cdot 5}{t - 5}$
26979	Evaluate the Integral	integral of x(x-7)^5 with respect to x	$\int x {(x - 7)}^{5} d x$
26980	Evaluate the Integral	integral of x(8x+5)^8 with respect to x	$\int x {(8 x + 5)}^{8} d x$
26981	Evaluate the Integral	integral of x(6x+7)^8 with respect to x	$\int x {(6 x + 7)}^{8} d x$
26982	Evaluate the Integral	integral of xsec(x^2)^2 with respect to x	$\int x \sec^{2} (x^{2}) d x$
26983	Evaluate the Integral	integral of tan(x)x with respect to x	$\int \tan (x) x d x$
26984	Evaluate the Integral	integral of tan(y) with respect to y	$\int \tan (y) d y$
26985	Evaluate the Integral	integral of tan(x)sec(x)^5 with respect to x	$\int \tan (x) \sec^{5} (x) d x$
26986	Evaluate the Integral	integral of t natural log of 2t with respect to t	$\int t \ln (2 t) d t$
26987	Evaluate the Integral	integral of t natural log of t with respect to t	$\int t \ln (t) d t$
26988	Evaluate the Integral	integral of tan(x)sin(x) with respect to x	$\int \tan (x) \sin (x) d x$
26989	Evaluate the Integral	integral of x(e^(x^2)+2) with respect to x	$\int x (e^{x^{2}} + 2) d x$
26990	Evaluate the Integral	integral of square root of 1+0.2x with respect to x	$\int \sqrt{1 + 0.2 x} d x$
26991	Evaluate the Integral	integral of x(1+ square root of x) with respect to x	$\int x (1 + \sqrt{x}) d x$
26992	Evaluate the Integral	integral of x(30x^2+90x) with respect to x	$\int x (30 x^{2} + 90 x) d x$
26993	Evaluate the Integral	integral of x(60x^2+30x) with respect to x	$\int x (60 x^{2} + 30 x) d x$
26994	Evaluate the Integral	integral of x(a-bx^2) with respect to x	$\int x (a - b x^{2}) d x$
26995	Evaluate the Integral	integral of x(csc(x))(cot(x)) with respect to x	$\int x (\csc (x)) (\cot (x)) d x$
26996	Evaluate the Integral	integral from x to pi of square root of 7+sec(5t) with respect to t	$\int_{x}^{π} \sqrt{7 + \sec (5 t)} d t$
26997	Evaluate the Integral	integral from x to 1 of et^2 with respect to t	$\int_{x}^{1} e t^{2} d t$
26998	Evaluate the Integral	d/((dx) integral from 2pi to cube root of x of cos(t) with respect to t)	$\frac{d}{(d x) \int_{2 π}^{\sqrt[3]{x}} \cos (t) d t}$
26999	Evaluate the Integral	square root of 2 integral from -pi/6 to pi/6 of sec(y)^2 with respect to y	$\sqrt{2} \int_{- \frac{π}{6}}^{\frac{π}{6}} \sec^{2} (y) d y$
27000	Evaluate the Integral	integral of te^(-7t^2) with respect to t	$\int t e^{- 7 t^{2}} d t$