Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
8501	Evaluate the Integral	integral of 1/(x(x-1)) with respect to x	$\int \frac{1}{x (x - 1)} d x$
8502	Evaluate the Integral	integral of 1/(x( natural log of x)^8) with respect to x	$\int \frac{1}{x \ln^{8} (x)} d x$
8503	Evaluate the Integral	integral of 1/(x square root of 25x^2-1) with respect to x	$\int \frac{1}{x \sqrt{25 x^{2} - 1}} d x$
8504	Evaluate the Integral	integral of 1/(x square root of 16x^2-1) with respect to x	$\int \frac{1}{x \sqrt{16 x^{2} - 1}} d x$
8505	Evaluate the Integral	integral of 1/(x natural log of x^8) with respect to x	$\int \frac{1}{x \ln (x^{8})} d x$
8506	Evaluate the Integral	integral of 1/(x natural log of 3x) with respect to x	$\int \frac{1}{x \ln (3 x)} d x$
8507	Evaluate the Integral	integral of 1/(y+1) with respect to y	$\int \frac{1}{y + 1} d y$
8508	Evaluate the Integral	integral of 1/v with respect to v	$\int \frac{1}{v} d v$
8509	Evaluate the Integral	integral of 1/(t square root of t) with respect to t	$\int \frac{1}{t \sqrt{t}} d t$
8510	Evaluate the Integral	integral of 1/r with respect to r	$\int \frac{1}{r} d r$
8511	Evaluate the Integral	integral of 1/(8x^3) with respect to x	$\int \frac{1}{8 x^{3}} d x$
8512	Evaluate the Integral	integral of 1/(7x^5) with respect to x	$\int \frac{1}{7 x^{5}} d x$
8513	Evaluate the Integral	integral of 1/(6-x) with respect to x	$\int \frac{1}{6 - x} d x$
8514	Evaluate the Integral	integral of 1/(1+sin(2x)) with respect to x	$\int \frac{1}{1 + \sin (2 x)} d x$
8515	Evaluate the Integral	integral of 1/(1+x^4) with respect to x	$\int \frac{1}{1 + x^{4}} d x$
8516	Evaluate the Integral	integral of 1/(10x^4) with respect to x	$\int \frac{1}{10 x^{4}} d x$
8517	Evaluate the Integral	integral of 1/(10x^5) with respect to x	$\int \frac{1}{10 x^{5}} d x$
8518	Evaluate the Integral	integral of 1/(x^8-x) with respect to x	$\int \frac{1}{x^{8} - x} d x$
8519	Evaluate the Integral	integral of 1/(x^2e^(3/x)) with respect to x	$\int \frac{1}{x^{2} e^{\frac{3}{x}}} d x$
8520	Evaluate the Integral	integral of 1/(x^11) with respect to x	$\int \frac{1}{x^{11}} d x$
8521	Evaluate the Integral	integral of 1/(x^2+4x+9) with respect to x	$\int \frac{1}{x^{2} + 4 x + 9} d x$
8522	Evaluate the Integral	integral of 1/(x^2+6x+10) with respect to x	$\int \frac{1}{x^{2} + 6 x + 10} d x$
8523	Evaluate the Integral	integral of 1/(x^2-3x+2) with respect to x	$\int \frac{1}{x^{2} - 3 x + 2} d x$
8524	Evaluate the Integral	integral of 1/(x^2-2x+10) with respect to x	$\int \frac{1}{x^{2} - 2 x + 10} d x$
8525	Find the Tangent Line at (π,0)	y=sin(sin(x)) , (pi,0)	$\int \frac{1}{e^{2 x} - 3 e^{x}} d x$
8526	Evaluate the Integral	integral of 1/(r^2) with respect to r	$\int \frac{1}{r^{2}} d r$
8527	Evaluate the Integral	integral of 1/(sec(x)^2) with respect to x	$\int \frac{1}{\sec^{2} (x)} d x$
8528	Evaluate the Integral	integral of 1/( square root of 1-16x^2) with respect to x	$\int \frac{1}{\sqrt{1 - 16 x^{2}}} d x$
8529	Evaluate the Integral	integral of 1/( square root of x^2-6x+13) with respect to x	$\int \frac{1}{\sqrt{x^{2} - 6 x + 13}} d x$
8530	Evaluate the Integral	integral of 1/(u^3) with respect to u	$\int \frac{1}{u^{3}} d u$
8531	Evaluate the Integral	integral of 1/( square root of 4-4x^2) with respect to x	$\int \frac{1}{\sqrt{4 - 4 x^{2}}} d x$
8532	Evaluate the Integral	integral of 1/( square root of 2x-5) with respect to x	$\int \frac{1}{\sqrt{2 x - 5}} d x$
8533	Find dy/dx	y=(x/3.8+3.8/x)(x^2+1)	$y = (\frac{x}{3.8} + \frac{3.8}{x}) (x^{2} + 1)$
8534	Evaluate the Integral	integral of 1/( square root of 9x^2-4) with respect to x	$\int \frac{1}{\sqrt{9 x^{2} - 4}} d x$
8535	Evaluate the Integral	integral of 1/( square root of 9-16x^2) with respect to x	$\int \frac{1}{\sqrt{9 - 16 x^{2}}} d x$
8536	Evaluate the Integral	integral of ( square root of x+4)/x with respect to x	$\int \frac{\sqrt{x + 4}}{x} d x$
8537	Evaluate the Integral	integral of (x^(1/3)-3)/(x^(2/3)) with respect to x	$\int \frac{x^{\frac{1}{3}} - 3}{x^{\frac{2}{3}}} d x$
8538	Evaluate the Integral	integral of ( square root of 4x^2-9)/x with respect to x	$\int \frac{\sqrt{4 x^{2} - 9}}{x} d x$
8539	Evaluate the Integral	integral of ( square root of 9-x^2)/x with respect to x	$\int \frac{\sqrt{9 - x^{2}}}{x} d x$
8540	Evaluate the Integral	integral of ( square root of x^2-25)/x with respect to x	$\int \frac{\sqrt{x^{2} - 25}}{x} d x$
8541	Evaluate the Integral	integral of (arctan(3x))/(1+9x^2) with respect to x	$\int \frac{\arctan (3 x)}{1 + 9 x^{2}} d x$
8542	Evaluate the Integral	integral of (x^2)/(e^(x^3)) with respect to x	$\int \frac{x^{2}}{e^{x^{3}}} d x$
8543	Evaluate the Integral	integral of (x^2)/((16-x^3)^2) with respect to x	$\int \frac{x^{2}}{{(16 - x^{3})}^{2}} d x$
8544	Find the Derivative - d/d@VAR	f(x)=5 square root of x	$f (x) = 5 \sqrt{x}$
8545	Find the Derivative - d/d?	sin(2theta)	$\sin (2 θ)$
8546	Evaluate the Integral	integral of (x^2+2x+3)/(x^3+3x^2+9x+1) with respect to x	$\int \frac{x^{2} + 2 x + 3}{x^{3} + 3 x^{2} + 9 x + 1} d x$
8547	Evaluate the Integral	integral of (x^2-1)/(x^3-3x+7) with respect to x	$\int \frac{x^{2} - 1}{x^{3} - 3 x + 7} d x$
8548	Evaluate the Integral	integral of (x^2-1)/(x+1) with respect to x	$\int \frac{x^{2} - 1}{x + 1} d x$
8549	Evaluate the Integral	integral of (x^2-4)/(x^3-12x+9) with respect to x	$\int \frac{x^{2} - 4}{x^{3} - 12 x + 9} d x$
8550	Evaluate the Integral	integral of 1/((25-x^2)^(3/2)) with respect to x	$\int \frac{1}{{(25 - x^{2})}^{\frac{3}{2}}} d x$
8551	Evaluate the Integral	integral of 1/(x^2)*cos(1/x) with respect to x	$\int \frac{1}{x^{2}} \cdot \cos (\frac{1}{x}) d x$
8552	Evaluate the Integral	integral of 1/((9-x^2)^(3/2)) with respect to x	$\int \frac{1}{{(9 - x^{2})}^{\frac{3}{2}}} d x$
8553	Evaluate the Integral	integral of (x^3-4x^2+7)/(x-4) with respect to x	$\int \frac{x^{3} - 4 x^{2} + 7}{x - 4} d x$
8554	Evaluate the Integral	integral of (x^4)/(x^5-3) with respect to x	$\int \frac{x^{4}}{x^{5} - 3} d x$
8555	Find the Derivative - d/d@VAR	f(x)=2x+3	$f (x) = 2 x + 3$
8556	Evaluate the Integral	integral of (x^3)/(x^2-1) with respect to x	$\int \frac{x^{3}}{x^{2} - 1} d x$
8557	Evaluate the Integral	integral of (x^3)/( square root of 1+x^2) with respect to x	$\int \frac{x^{3}}{\sqrt{1 + x^{2}}} d x$
8558	Evaluate the Integral	integral of (x^3)/( square root of 16-x^2) with respect to x	$\int \frac{x^{3}}{\sqrt{16 - x^{2}}} d x$
8559	Evaluate the Integral	integral of (x^3+125)/(x+5) with respect to x	$\int \frac{x^{3} + 125}{x + 5} d x$
8560	Find the Tangent Line at (3π,0)	y=sin(sin(x)) , (3pi,0)	$\int \frac{5 - e^{x}}{e^{2 x}} d x$
8561	Evaluate the Integral	integral of (4+5x^(3/2))/( square root of x) with respect to x	$\int \frac{4 + 5 x^{\frac{3}{2}}}{\sqrt{x}} d x$
8562	Evaluate the Integral	integral of (4x)/(x^2+1) with respect to x	$\int \frac{4 x}{x^{2} + 1} d x$
8563	Evaluate the Integral	integral of 4/(4x^2+4x+65) with respect to x	$\int \frac{4}{4 x^{2} + 4 x + 65} d x$
8564	Evaluate the Integral	integral of 4/(x natural log of x) with respect to x	$\int \frac{4}{x \ln (x)} d x$
8565	Evaluate the Integral	integral of (4x^3+3)/(x^4+3x) with respect to x	$\int \frac{4 x^{3} + 3}{x^{4} + 3 x} d x$
8566	Evaluate the Integral	integral of (4x^3-5 square root of x)/x with respect to x	$\int \frac{4 x^{3} - 5 \sqrt{x}}{x} d x$
8567	Evaluate the Integral	integral of (5x+1)/((2x+1)(x-1)) with respect to x	$\int \frac{5 x + 1}{(2 x + 1) (x - 1)} d x$
8568	Evaluate the Integral	integral of (5x+3)/(x^3-2x^2-3x) with respect to x	$\int \frac{5 x + 3}{x^{3} - 2 x^{2} - 3 x} d x$
8569	Evaluate the Integral	integral of (6x^3)/(2x^4+1) with respect to x	$\int \frac{6 x^{3}}{2 x^{4} + 1} d x$
8570	Evaluate the Integral	integral of 6^(5x) with respect to x	$\int 6^{5 x} d x$
8571	Evaluate the Integral	integral of 7/(x^2+1) with respect to x	$\int \frac{7}{x^{2} + 1} d x$
8572	Evaluate the Integral	integral of 7/(2x^(9/4)) with respect to x	$\int \frac{7}{2 x^{\frac{9}{4}}} d x$
8573	Evaluate the Integral	integral of 7/(x-4) with respect to x	$\int \frac{7}{x - 4} d x$
8574	Evaluate the Integral	integral of (6arcsin(x))/( square root of 1-x^2) with respect to x	$\int \frac{6 \arcsin (x)}{\sqrt{1 - x^{2}}} d x$
8575	Evaluate the Integral	integral of (8x^3-1)/(2x-1) with respect to x	$\int \frac{8 x^{3} - 1}{2 x - 1} d x$
8576	Evaluate the Integral	integral of (cos(x))/(1+2sin(x)) with respect to x	$\int \frac{\cos (x)}{1 + 2 \sin (x)} d x$
8577	Evaluate the Integral	integral of (cos(t))/(1+sin(t)) with respect to t	$\int \frac{\cos (t)}{1 + \sin (t)} d t$
8578	Evaluate the Integral	integral of cos(2x)^3sin(2x) with respect to x	$\int \cos^{3} (2 x) \sin (2 x) d x$
8579	Evaluate the Integral	integral of (cos(x)-3)/(6x-2sin(x)) with respect to x	$\int \frac{\cos (x) - 3}{6 x - 2 \sin (x)} d x$
8580	Evaluate the Integral	integral of arccos(x) with respect to x	$\int \arccos (x) d x$
8581	Evaluate the Function	f(x) = square root of 4-x at a=0	$\int \frac{\cos (x) + \sin (2 x)}{\sin (x)} d x$
8582	Evaluate the Integral	integral of cos(x)^(1/2) with respect to x	$\int {\cos (x)}^{\frac{1}{2}} d x$
8583	Evaluate the Integral	integral of (cos(x^(1/2)))/(x^(1/2)) with respect to x	$\int \frac{\cos (x^{\frac{1}{2}})}{x^{\frac{1}{2}}} d x$
8584	Evaluate the Integral	integral of (1-2 cube root of z)/( cube root of z) with respect to z	$\int \frac{1 - 2 \sqrt[3]{z}}{\sqrt[3]{z}} d z$
8585	Evaluate the Integral	integral of (10x^3-5x)/( square root of x^4-x^2+6) with respect to x	$\int \frac{10 x^{3} - 5 x}{\sqrt{x^{4} - x^{2} + 6}} d x$
8586	Evaluate the Integral	integral of 15^x with respect to x	$\int 15^{x} d x$
8587	Evaluate the Integral	integral of (16x^3)/(4x^4+3) with respect to x	$\int \frac{16 x^{3}}{4 x^{4} + 3} d x$
8588	Evaluate the Integral	integral of 14^x with respect to x	$\int 14^{x} d x$
8589	Evaluate the Integral	integral of 12/(1+9x^2) with respect to x	$\int \frac{12}{1 + 9 x^{2}} d x$
8590	Evaluate the Integral	integral of (12x+18)/( square root of x^2+3x-4) with respect to x	$\int \frac{12 x + 18}{\sqrt{x^{2} + 3 x - 4}} d x$
8591	Evaluate the Integral	integral of -2000/(x^2) with respect to x	$\int - \frac{2000}{x^{2}} d x$
8592	Evaluate the Integral	integral of -(2200x)/( square root of 25-x^2) with respect to x	$\int - \frac{2200 x}{\sqrt{25 - x^{2}}} d x$
8593	Evaluate the Integral	integral of 2/((2x-7)^2) with respect to x	$\int \frac{2}{{(2 x - 7)}^{2}} d x$
8594	Evaluate the Integral	integral of 3/2* square root of x with respect to x	$\int \frac{3}{2} \cdot \sqrt{x} d x$
8595	Evaluate the Integral	integral of 3/(4x^2+4) with respect to x	$\int \frac{3}{4 x^{2} + 4} d x$
8596	Evaluate the Integral	integral of (3x+2)/( square root of 1-x^2) with respect to x	$\int \frac{3 x + 2}{\sqrt{1 - x^{2}}} d x$
8597	Evaluate the Integral	integral of 37/(x^2) with respect to x	$\int \frac{37}{x^{2}} d x$
8598	Evaluate the Integral	integral of (3t)/2 with respect to t	$\int \frac{3 t}{2} d t$
8599	Evaluate the Integral	integral of (2x)/(x^2+6x+13) with respect to x	$\int \frac{2 x}{x^{2} + 6 x + 13} d x$
8600	Evaluate the Integral	integral of (2x+1)/(x^2+x+1) with respect to x	$\int \frac{2 x + 1}{x^{2} + x + 1} d x$