Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
5101	Evaluate the Integral	integral from 0 to pi of sin(x)^2 with respect to x	$\int_{0}^{π} \sin^{2} (x) d x$
5102	Evaluate the Integral	integral from 0 to pi of sec(t/4)^2 with respect to t	$\int_{0}^{π} \sec^{2} (\frac{t}{4}) d t$
5103	Evaluate the Integral	integral from 0 to pi of x^2cos(4x) with respect to x	$\int_{0}^{π} x^{2} \cos (4 x) d x$
5104	Evaluate the Integral	integral from 0 to pi of 2cos(x) with respect to x	$\int_{0}^{π} 2 \cos (x) d x$
5105	Evaluate the Integral	integral from 0 to pi of 2sin(x) with respect to x	$\int_{0}^{π} 2 \sin (x) d x$
5106	Evaluate the Integral	integral from 0 to 2 of 4-x^2 with respect to x	$\int_{0}^{2} 4 - x^{2} d x$
5107	Evaluate the Integral	integral from 0 to 2 of x square root of 4-x^2 with respect to x	$\int_{0}^{2} x \sqrt{4 - x^{2}} d x$
5108	Evaluate the Integral	integral from 0 to 3 of e^t-e^(-t) with respect to t	$\int_{0}^{3} e^{t} - e^{- t} d t$
5109	Evaluate the Integral	integral from 0 to 3 of x^3-6x with respect to x	$\int_{0}^{3} x^{3} - 6 x d x$
5110	Evaluate the Integral	integral from 0 to 4 of x/( square root of x^2+9) with respect to x	$\int_{0}^{4} \frac{x}{\sqrt{x^{2} + 9}} d x$
5111	Evaluate the Integral	integral from 0 to 4 of 1/(2+t) with respect to tdt	$\int_{0}^{4} \frac{1}{2 + t} d t d t$
5112	Evaluate the Integral	integral from 0 to 3 of 2x-3 with respect to x	$\int_{0}^{3} 2 x - 3 d x$
5113	Evaluate the Integral	integral from 0 to 3 of square root of x+1 with respect to x	$\int_{0}^{3} \sqrt{x + 1} d x$
5114	Evaluate the Integral	integral from 0 to 6 of 1/2x with respect to x	$\int_{0}^{6} \frac{1}{2} x d x$
5115	Evaluate the Integral	integral from 0 to 5 of 1/( square root of 3x+1) with respect to x	$\int_{0}^{5} \frac{1}{\sqrt{3 x + 1}} d x$
5116	Evaluate the Integral	integral from 0 to 4 of x square root of x^2+9 with respect to x	$\int_{0}^{4} x \sqrt{x^{2} + 9} d x$
5117	Evaluate the Integral	integral from 0 to 4 of 8 with respect to x	$\int_{0}^{4} 8 d x$
5118	Evaluate the Integral	integral from 0 to 4 of -x^2+4x with respect to x	$\int_{0}^{4} - x^{2} + 4 x d x$
5119	Evaluate the Integral	integral from 0 to 4 of x^2 square root of 16-x^2 with respect to x	$\int_{0}^{4} x^{2} \sqrt{16 - x^{2}} d x$
5120	Evaluate the Integral	integral from 0 to pi of 1+cos(x) with respect to x	$\int_{0}^{π} 1 + \cos (x) d x$
5121	Evaluate the Integral	integral from 0 to pi of 8+sin(x) with respect to x	$\int_{0}^{π} 8 + \sin (x) d x$
5122	Evaluate the Integral	integral from 0 to natural log of 2 of e^(3x) with respect to x	$\int_{0}^{\ln (2)} e^{3 x} d x$
5123	Evaluate the Integral	integral from 0 to 7 of square root of 4+3x with respect to x	$\int_{0}^{7} \sqrt{4 + 3 x} d x$
5124	Evaluate the Integral	integral from 0 to 8 of 8-4 cube root of x with respect to x	$\int_{0}^{8} 8 - 4 \sqrt[3]{x} d x$
5125	Evaluate the Integral	integral from 0 to 8 of cube root of x with respect to x	$\int_{0}^{8} \sqrt[3]{x} d x$
5126	Evaluate the Integral	integral from 0 to 1 of x( cube root of x+ fourth root of x) with respect to x	$\int_{0}^{1} x (\sqrt[3]{x} + \sqrt[4]{x}) d x$
5127	Evaluate the Integral	integral from 0 to 1 of x(4 cube root of x+5 fourth root of x) with respect to x	$\int_{0}^{1} x (4 \sqrt[3]{x} + 5 \sqrt[4]{x}) d x$
5128	Evaluate the Integral	integral from 0 to 1 of 4x^3e^(x^4) with respect to x	$\int_{0}^{1} 4 x^{3} e^{x^{4}} d x$
5129	Evaluate the Integral	integral from 0 to 1 of 3 cube root of x with respect to x	$\int_{0}^{1} 3 \sqrt[3]{x} d x$
5130	Evaluate the Integral	integral from 0 to 1 of 6x^5e^(x^6) with respect to x	$\int_{0}^{1} 6 x^{5} e^{x^{6}} d x$
5131	Evaluate the Integral	integral from 0 to 1 of arcsin(x) with respect to x	$\int_{0}^{1} \arcsin (x) d x$
5132	Evaluate the Integral	integral from 0 to 1 of natural log of x^2+1 with respect to x	$\int_{0}^{1} \ln (x^{2} + 1) d x$
5133	Evaluate the Integral	integral from 0 to 1 of 7xe^(5x) with respect to x	$\int_{0}^{1} 7 x e^{5 x} d x$
5134	Evaluate the Integral	integral from 0 to 1 of 8 eighth root of x with respect to x	$\int_{0}^{1} 8 \sqrt[8]{x} d x$
5135	Evaluate the Integral	integral from 0 to 1 of y/(e^(2y)) with respect to y	$\int_{0}^{1} \frac{y}{e^{2 y}} d y$
5136	Evaluate the Integral	integral from 0 to 1 of 1111 root of x with respect to x	$\int_{0}^{1} 11 \sqrt[11]{x} d x$
5137	Evaluate the Integral	integral from 0 to 1 of xe^(-x) with respect to x	$\int_{0}^{1} x e^{- x} d x$
5138	Evaluate the Integral	integral from 0 to 12 of 4x^2 with respect to x	$\int_{0}^{12} 4 x^{2} d x$
5139	Evaluate the Integral	integral from 0 to 16 of 3 square root of x with respect to x	$\int_{0}^{16} 3 \sqrt{x} d x$
5140	Evaluate the Integral	integral from 0 to 2 of e^(-2t) with respect to t	$\int_{0}^{2} e^{- 2 t} d t$
5141	Evaluate the Integral	integral from 0 to 2 of x^2 square root of x^3+1 with respect to x	$\int_{0}^{2} x^{2} \sqrt{x^{3} + 1} d x$
5142	Find the Derivative - d/d@VAR	f(x)=(10-cos(x))/(10+sin(x))	$f (x) = \frac{10 - \cos (x)}{10 + \sin (x)}$
5143	Evaluate the Integral	integral from 0 to 1 of square root of x^2-2x+1 with respect to x	$\int_{0}^{1} \sqrt{x^{2} - 2 x + 1} d x$
5144	Evaluate the Integral	integral from 0 to 1 of square root of x^2+1 with respect to x	$\int_{0}^{1} \sqrt{x^{2} + 1} d x$
5145	Evaluate the Integral	integral from 0 to 1 of e^x-x with respect to x	$\int_{0}^{1} e^{x} - x d x$
5146	Evaluate the Integral	integral from 0 to 1 of x^2(3x^3-1)^4 with respect to x	$\int_{0}^{1} x^{2} {(3 x^{3} - 1)}^{4} d x$
5147	Evaluate the Summation	sum from n=1 to 14 of 2n+1	$\sum_{n = 1}^{14} 2 n + 1$
5148	Evaluate the Integral	integral from 0 to 1 of x^3(2x^4+1)^2 with respect to x	$\int_{0}^{1} x^{3} {(2 x^{4} + 1)}^{2} d x$
5149	Evaluate the Integral	integral from 0 to 1 of x^2(1+2x^3)^5 with respect to x	$\int_{0}^{1} x^{2} {(1 + 2 x^{3})}^{5} d x$
5150	Evaluate the Integral	integral from 0 to fourth root of pi of x^3cos(x^4) with respect to x	$\int_{0}^{\sqrt[4]{π}} x^{3} \cos (x^{4}) d x$
5151	Evaluate the Integral	integral from 0 to 0 of 3-3x with respect to x	$\int_{0}^{0} 3 - 3 x d x$
5152	Evaluate the Integral	integral from -0 to -0 of -x with respect to x	$\int_{- 0}^{- 0} - x d x$
5153	Evaluate the Integral	integral from 0 to square root of 19 of 7x cube root of 8+x^2 with respect to x	$\int_{0}^{\sqrt{19}} 7 x \sqrt[3]{8 + x^{2}} d x$
5154	Evaluate the Integral	integral from 0 to pi/4 of tan(x) with respect to x	$\int_{0}^{\frac{π}{4}} \tan (x) d x$
5155	Evaluate the Integral	integral from 0 to pi/4 of sec(x) with respect to x	$\int_{0}^{\frac{π}{4}} \sec (x) d x$
5156	Evaluate the Integral	integral from 0 to pi/4 of cos(x)-sin(x) with respect to x	$\int_{0}^{\frac{π}{4}} \cos (x) - \sin (x) d x$
5157	Evaluate the Integral	integral from 0 to pi/3 of tan(x) with respect to x	$\int_{0}^{\frac{π}{3}} \tan (x) d x$
5158	Evaluate the Integral	integral from 0 to pi/3 of sec(x)tan(x) with respect to x	$\int_{0}^{\frac{π}{3}} \sec (x) \tan (x) d x$
5159	Evaluate the Integral	integral from 0 to pi/4 of (e^(tan(x)))/(cos(x)^2) with respect to x	$\int_{0}^{\frac{π}{4}} \frac{e^{\tan (x)}}{\cos^{2} (x)} d x$
5160	Evaluate the Integral	integral of x square root of 9-5x^2 with respect to x	$\int x \sqrt{9 - 5 x^{2}} d x$
5161	Evaluate the Integral	integral of x square root of x+9 with respect to x	$\int x \sqrt{x + 9} d x$
5162	Evaluate the Integral	integral of xcos(2x)^2 with respect to x	$\int x \cos^{2} (2 x) d x$
5163	Evaluate the Integral	integral of xcos(x)^2 with respect to x	$\int x \cos^{2} (x) d x$
5164	Evaluate the Integral	integral of x(4x-1)^4 with respect to x	$\int x {(4 x - 1)}^{4} d x$
5165	Evaluate the Integral	integral of x(6x+5)^8 with respect to x	$\int x {(6 x + 5)}^{8} d x$
5166	Evaluate the Integral	integral of x(4x+5)^8 with respect to x	$\int x {(4 x + 5)}^{8} d x$
5167	Evaluate the Integral	integral of tcos(t) with respect to t	$\int t \cos (t) d t$
5168	Evaluate the Integral	integral of tsin(t) with respect to t	$\int t \sin (t) d t$
5169	Evaluate the Integral	integral of xcos(3x^2) with respect to x	$\int x \cos (3 x^{2}) d x$
5170	Evaluate the Integral	integral of p(p+7)^5 with respect to p	$\int p {(p + 7)}^{5} d p$
5171	Evaluate the Integral	integral of sin(1/2x) with respect to x	$\int \sin (\frac{1}{2} x) d x$
5172	Evaluate the Integral	integral of sec(y)(tan(y)-sec(y)) with respect to y	$\int \sec (y) (\tan (y) - \sec (y)) d y$
5173	Evaluate the Integral	integral of sec(5x)tan(5x) with respect to x	$\int \sec (5 x) \tan (5 x) d x$
5174	Evaluate the Integral	integral of sec(1-x)tan(1-x) with respect to x	$\int \sec (1 - x) \tan (1 - x) d x$
5175	Evaluate the Integral	integral of sec(8x)tan(8x) with respect to x	$\int \sec (8 x) \tan (8 x) d x$
5176	Evaluate the Integral	integral of sin(x)cos(cos(x)) with respect to x	$\int \sin (x) \cos (\cos (x)) d x$
5177	Evaluate the Integral	integral of sin(x)tan(x) with respect to x	$\int \sin (x) \tan (x) d x$
5178	Evaluate the Integral	integral of sin(h(x/5)) with respect to x	$\int \sinh (\frac{x}{5}) d x$
5179	Evaluate the Integral	integral of tan(x^3) with respect to x	$\int \tan (x^{3}) d x$
5180	Evaluate the Integral	integral of tan(u) with respect to u	$\int \tan (u) d u$
5181	Evaluate the Integral	integral of tan(5x) with respect to x	$\int \tan (5 x) d x$
5182	Evaluate the Integral	integral of sin(-2x) with respect to x	$\int \sin (- 2 x) d x$
5183	Evaluate the Integral	integral of sin(3x)cos(3x) with respect to x	$\int \sin (3 x) \cos (3 x) d x$
5184	Evaluate the Integral	integral of sin(3x)sin(2x) with respect to x	$\int \sin (3 x) \sin (2 x) d x$
5185	Evaluate the Integral	integral of sin(3y)+cos(5y) with respect to y	$\int \sin (3 y) + \cos (5 y) d y$
5186	Evaluate the Integral	integral of sin(t) with respect to t	$\int \sin (t) d t$
5187	Evaluate the Integral	integral of sin(pit) with respect to t	$\int \sin (π t) d t$
5188	Evaluate the Integral	integral of sin(u) with respect to u	$\int \sin (u) d u$
5189	Evaluate the Integral	integral of sin(9x) with respect to x	$\int \sin (9 x) d x$
5190	Evaluate the Integral	integral of cos(2t) with respect to t	$\int \cos (2 t) d t$
5191	Evaluate the Integral	integral of cos(9x) with respect to x	$\int \cos (9 x) d x$
5192	Evaluate the Integral	integral from a to b of 1/4x^2 with respect to x	$\int_{a}^{b} \frac{1}{4} x^{2} d x$
5193	Evaluate the Integral	integral of arctan( square root of x) with respect to x	$\int \arctan (\sqrt{x}) d x$
5194	Evaluate the Integral	integral of arccos(2x) with respect to x	$\int \arccos (2 x) d x$
5195	Evaluate the Integral	integral of natural log of 8x with respect to x	$\int \ln (8 x) d x$
5196	Evaluate the Integral	integral of natural log of 1-x with respect to x	$\int \ln (1 - x) d x$
5197	Evaluate the Integral	integral of natural log of 1+x with respect to x	$\int \ln (1 + x) d x$
5198	Evaluate the Integral	integral of csc(3x) with respect to x	$\int \csc (3 x) d x$
5199	Evaluate the Integral	integral of csc(2x)cot(2x) with respect to x	$\int \csc (2 x) \cot (2 x) d x$
5200	Evaluate the Integral	integral of cot(3x) with respect to x	$\int \cot (3 x) d x$