Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
8301	Evaluate the Summation	sum from k=1 to 16 of 2k+7	$\sum_{k = 1}^{16} 2 k + 7$
8302	Evaluate the Summation	sum from k=1 to 2 of (15k)/(k+4)	$\sum_{k = 1}^{2} \frac{15 k}{k + 4}$
8303	Evaluate the Summation	sum from j=3 to 5 of 1/j	$\sum_{j = 3}^{5} \frac{1}{j}$
8304	Evaluate the Summation	sum from k=1 to 5 of cos(kpi)	$\sum_{k = 1}^{5} \cos (k π)$
8305	Evaluate the Summation	sum from k=1 to 5 of sin(kpi)	$\sum_{k = 1}^{5} \sin (k π)$
8306	Evaluate the Summation	sum from k=1 to 8 of k(6k+7)	$\sum_{k = 1}^{8} k (6 k + 7)$
8307	Find the Critical Points	f(x)=4x^3-12x	$f (x) = 4 x^{3} - 12 x$
8308	Evaluate the Limit	limit as x approaches -8 of x/(4x-1)	$lim_{x \to - 8} \frac{x}{4 x - 1}$
8309	Evaluate Using L'Hospital's Rule	( limit as x approaches 3 of x-3)/(x^2-9)	$\frac{lim_{x \to 3} x - 3}{x^{2} - 9}$
8310	Evaluate Using L'Hospital's Rule	( limit as x approaches 0 of e^x-e^(-x)-2x)/(x-sin(x))	$\frac{lim_{x \to 0} e^{x} - e^{- x} - 2 x}{x - \sin (x)}$
8311	Evaluate Using L'Hospital's Rule	( limit as x approaches pi/2 of cos(x))/(1-sin(x))	$\frac{lim_{x \to \frac{π}{2}} \cos (x)}{1 - \sin (x)}$
8312	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-1)/x	$lim_{x \to 0} \frac{e^{x} - 1}{x}$
8313	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of ( natural log of x+1)/x	$lim_{x \to 0} \frac{\ln (x + 1)}{x}$
8314	Evaluate Using L'Hospital's Rule	limit as x approaches pi/2 of (x-pi/2)sec(x)	$lim_{x \to \frac{π}{2}} (x - \frac{π}{2}) \sec (x)$
8315	Evaluate Using L'Hospital's Rule	( limit as x approaches 0 of x)/(arctan(4x))	$\frac{lim_{x \to 0} x}{\arctan (4 x)}$
8316	Evaluate Using L'Hospital's Rule	limit as x approaches 8 of ( natural log of x)/(x^2)	$lim_{x \to 8} \frac{\ln (x)}{x^{2}}$
8317	Identify the Sequence	11/2 , 11/3 , 11/4 , 11/5 , 11/6	$\frac{11}{2}$ , $\frac{11}{3}$ , $\frac{11}{4}$ , $\frac{11}{5}$ , $\frac{11}{6}$
8318	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of ( natural log of x^2)/(x^2-1)	$lim_{x \to 1} \frac{\ln (x^{2})}{x^{2} - 1}$
8319	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of cot(3x)sin(6x)	$lim_{x \to 0} \cot (3 x) \sin (6 x)$
8320	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-e^(-x))/(sin(x))	$lim_{x \to 0} \frac{e^{x} - e^{- x}}{\sin (x)}$
8321	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (1-cos(x))/(sin(x))	$lim_{x \to 0} \frac{1 - \cos (x)}{\sin (x)}$
8322	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of x/(tan(x))	$lim_{x \to 0} \frac{x}{\tan (x)}$
8323	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(7x))/(tan(3x))	$lim_{x \to 0} \frac{\sin (7 x)}{\tan (3 x)}$
8324	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (sin(x))/(x+tan(x))	$lim_{x \to 0} \frac{\sin (x)}{x + \tan (x)}$
8325	Find the Local Maxima and Minima	sin(x)+cos(x)	$\sin (x) + \cos (x)$
8326	Evaluate the Integral	integral of (x-1)^25 with respect to x	$\int {(x - 1)}^{25} d x$
8327	Evaluate the Integral	integral of (x-4x^8)^6 with respect to x	$\int {(x - 4 x^{8})}^{6} d x$
8328	Evaluate the Integral	integral of (csc(x)-tan(x))^2 with respect to x	$\int {(\csc (x) - \tan (x))}^{2} d x$
8329	Evaluate the Integral	integral of (4x-3)^2 with respect to x	$\int {(4 x - 3)}^{2} d x$
8330	Evaluate the Integral	integral of (4x-3)^4 with respect to x	$\int {(4 x - 3)}^{4} d x$
8331	Evaluate the Integral	integral of (5-3x)^-1 with respect to x	$\int {(5 - 3 x)}^{- 1} d x$
8332	Evaluate the Integral	integral of (3x+1)^4 with respect to x	$\int {(3 x + 1)}^{4} d x$
8333	Evaluate the Integral	integral of (3x-1)^5 with respect to x	$\int {(3 x - 1)}^{5} d x$
8334	Evaluate the Integral	integral of (e^(2x))/(4+e^(2x)) with respect to x	$\int \frac{e^{2 x}}{4 + e^{2 x}} d x$
8335	Evaluate the Integral	integral of (e^u)/((2-e^u)^2) with respect to u	$\int \frac{e^{u}}{{(2 - e^{u})}^{2}} d u$
8336	Evaluate the Integral	integral of (e^t-t)/2 with respect to t	$\int \frac{e^{t} - t}{2} d t$
8337	Evaluate the Integral	integral of (e^r)/(1+e^r) with respect to r	$\int \frac{e^{r}}{1 + e^{r}} d r$
8338	Evaluate the Integral	integral of (e^x)/(1-e^x) with respect to x	$\int \frac{e^{x}}{1 - e^{x}} d x$
8339	Evaluate the Integral	integral of (e^x)/( square root of e^x+1) with respect to x	$\int \frac{e^{x}}{\sqrt{e^{x} + 1}} d x$
8340	Evaluate the Integral	integral of (cos(x)^4)/(sin(x)^6) with respect to x	$\int \frac{\cos^{4} (x)}{\sin^{6} (x)} d x$
8341	Evaluate the Integral	integral of (e^(3/x))/(x^2) with respect to x	$\int \frac{e^{\frac{3}{x}}}{x^{2}} d x$
8342	Evaluate the Integral	integral of (2^x)/( natural log of 2) with respect to x	$\int \frac{2^{x}}{\ln (2)} d x$
8343	Evaluate the Integral	integral of (x^2-3)^5(2x) with respect to x	$\int {(x^{2} - 3)}^{5} (2 x) d x$
8344	Evaluate the Integral	integral of (x^2-4x+4)^(4/3) with respect to x	$\int {(x^{2} - 4 x + 4)}^{\frac{4}{3}} d x$
8345	Evaluate the Integral	integral of sin(6y)+cos(5y) with respect to y	$\int \sin (6 y) + \cos (5 y) d y$
8346	Evaluate the Integral	integral of (x+13) square root of 26x+x^2 with respect to x	$\int (x + 13) \sqrt{26 x + x^{2}} d x$
8347	Evaluate the Integral	integral of (x+14) square root of 28x+x^2 with respect to x	$\int (x + 14) \sqrt{28 x + x^{2}} d x$
8348	Evaluate the Integral	integral of (x-1)sin(pix) with respect to x	$\int (x - 1) \sin (π x) d x$
8349	Evaluate the Integral	integral of (x+4) square root of 3-x with respect to x	$\int (x + 4) \sqrt{3 - x} d x$
8350	Evaluate the Integral	integral of (3t+2)^2.4 with respect to t	$\int {(3 t + 2)}^{2.4} d t$
8351	Evaluate the Integral	integral of (2x^2-x+4)/(x^3+4x) with respect to x	$\int \frac{2 x^{2} - x + 4}{x^{3} + 4 x} d x$
8352	Evaluate the Integral	integral of (1+sin(x))^(5/2)cos(x) with respect to x	$\int {(1 + \sin (x))}^{\frac{5}{2}} \cos (x) d x$
8353	Evaluate the Integral	integral of (x^8+6)^7(8x^7) with respect to x	$\int {(x^{8} + 6)}^{7} (8 x^{7}) d x$
8354	Evaluate the Integral	integral of e^(10u)+4 with respect to u udu	$\int e^{10 u} + 4 d u$ udu
8355	Evaluate the Integral	integral of e^(8x)+e^(-9x) with respect to x	$\int e^{8 x} + e^{- 9 x} d x$
8356	Evaluate the Integral	integral of t^3+e^(5t) with respect to t	$\int t^{3} + e^{5 t} d t$
8357	Evaluate the Integral	integral of (t^2+t)cos(3t) with respect to t	$\int (t^{2} + t) \cos (3 t) d t$
8358	Evaluate the Integral	integral of 11 root of x+12 root of x with respect to x	$\int \sqrt[11]{x} + \sqrt[12]{x} d x$
8359	Evaluate the Integral	integral of square root of r-1/(r^3) with respect to r	$\int \sqrt{r} - \frac{1}{r^{3}} d r$
8360	Evaluate the Integral	integral of x^2-2x+5 with respect to x	$\int x^{2} - 2 x + 5 d x$
8361	Evaluate the Integral	integral of (x^2+7x)cos(x) with respect to x	$\int (x^{2} + 7 x) \cos (x) d x$
8362	Evaluate the Integral	integral of x^4-9/2* square root of x+x^(-4/3) with respect to x	$\int x^{4} - \frac{9}{2} \cdot \sqrt{x} + x^{- \frac{4}{3}} d x$
8363	Evaluate the Integral	integral of x^3-5x with respect to x	$\int x^{3} - 5 x d x$
8364	Evaluate the Integral	integral of fifth root of x+ sixth root of x with respect to x	$\int \sqrt[5]{x} + \sqrt[6]{x} d x$
8365	Evaluate the Integral	integral of x/6+6/x with respect to x	$\int \frac{x}{6} + \frac{6}{x} d x$
8366	Evaluate the Integral	integral of (x^2+4x)cos(x) with respect to x	$\int (x^{2} + 4 x) \cos (x) d x$
8367	Evaluate the Integral	integral of (x^2+5x+6)cos(2x) with respect to x	$\int (x^{2} + 5 x + 6) \cos (2 x) d x$
8368	Evaluate the Integral	integral of 1/(x^6)-x^6-1/4 with respect to x	$\int \frac{1}{x^{6}} - x^{6} - \frac{1}{4} d x$
8369	Evaluate the Integral	integral of 13/( square root of x) with respect to x	$\int \frac{13}{\sqrt{x}} d x$
8370	Evaluate the Integral	integral of 2/x+2e^x with respect to x	$\int \frac{2}{x} + 2 e^{x} d x$
8371	Evaluate the Integral	integral of 2/(x-4)-3/(2x+1) with respect to x	$\int \frac{2}{x - 4} - \frac{3}{2 x + 1} d x$
8372	Evaluate the Integral	integral of 6/( square root of x)+6 square root of x with respect to x	$\int \frac{6}{\sqrt{x}} + 6 \sqrt{x} d x$
8373	Find dy/dx	y=x^11e^x	$y = x^{11} e^{x}$
8374	Evaluate the Integral	integral of (t^3)/3+1/(4t^2) with respect to t	$\int \frac{t^{3}}{3} + \frac{1}{4 t^{2}} d t$
8375	Evaluate the Integral	integral of (t^2)/2-2/(t^2) with respect to t	$\int \frac{t^{2}}{2} - \frac{2}{t^{2}} d t$
8376	Evaluate the Integral	integral of 3x-4 with respect to x	$\int 3 x - 4 d x$
8377	Evaluate the Integral	integral of 4x^2-6x with respect to x	$\int 4 x^{2} - 6 x d x$
8378	Evaluate the Integral	integral of 6+u+u^2 with respect to u	$\int 6 + u + u^{2} d u$
8379	Evaluate the Integral	integral of 9x^2+2x-5 with respect to x	$\int 9 x^{2} + 2 x - 5 d x$
8380	Evaluate the Integral	integral of -9t^2+14t-2 with respect to t	$\int - 9 t^{2} + 14 t - 2 d t$
8381	Evaluate the Integral	integral of 9x^2-8x+3 with respect to x	$\int 9 x^{2} - 8 x + 3 d x$
8382	Evaluate the Integral	integral of 9x^2-7x+4 with respect to x	$\int 9 x^{2} - 7 x + 4 d x$
8383	Evaluate the Integral	integral of (1+x^2)(2-x) with respect to x	$\int (1 + x^{2}) (2 - x) d x$
8384	Evaluate the Integral	integral of x^6+e^(3x) with respect to x	$\int x^{6} + e^{3 x} d x$
8385	Evaluate the Integral	integral of x^4-2x^3+1/(x^2) with respect to x	$\int x^{4} - 2 x^{3} + \frac{1}{x^{2}} d x$
8386	Evaluate the Integral	integral of x^4-3 square root of x+x^(-5/4) with respect to x	$\int x^{4} - 3 \sqrt{x} + x^{- \frac{5}{4}} d x$
8387	Evaluate the Integral	integral of 10x+3 with respect to x	$\int 10 x + 3 d x$
8388	Evaluate the Integral	integral of 12x^2-9x+3 with respect to x	$\int 12 x^{2} - 9 x + 3 d x$
8389	Evaluate the Integral	integral of 15x square root of x+2 square root of x with respect to x	$\int 15 x \sqrt{x} + 2 \sqrt{x} d x$
8390	Evaluate the Integral	integral of 15s^4-8s with respect to s	$\int 15 s^{4} - 8 s d s$
8391	Evaluate the Integral	integral of 16x+5 with respect to x	$\int 16 x + 5 d x$
8392	Evaluate the Integral	integral of 16x+9 with respect to x	$\int 16 x + 9 d x$
8393	Evaluate the Integral	integral of 18x+5 with respect to x	$\int 18 x + 5 d x$
8394	Evaluate the Integral	integral of 18x+7 with respect to x	$\int 18 x + 7 d x$
8395	Evaluate the Integral	integral of (2x+5)(x^2+5x)^7 with respect to x	$\int (2 x + 5) {(x^{2} + 5 x)}^{7} d x$
8396	Evaluate the Integral	integral of 2z+3 with respect to z	$\int 2 z + 3 d z$
8397	Evaluate the Integral	integral of 2x^5-7x^3+9 with respect to x	$\int 2 x^{5} - 7 x^{3} + 9 d x$
8398	Evaluate the Integral	integral of 2x^5-7x^3+5 with respect to x	$\int 2 x^{5} - 7 x^{3} + 5 d x$
8399	Evaluate the Integral	integral of 24 cube root of x^5-24/( cube root of x^5) with respect to x	$\int 24 \sqrt[3]{x^{5}} - \frac{24}{\sqrt[3]{x^{5}}} d x$
8400	Evaluate the Integral	integral of -24x^5-4x+15x^-4 with respect to x	$\int - 24 x^{5} - 4 x + 15 x^{- 4} d x$