Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
1501	Find the Derivative - d/dx	cos(x)^5	$\cos^{5} (x)$
1502	Find the Derivative - d/dx	(3-xe^x)/(x+e^x)	$\frac{3 - x e^{x}}{x + e^{x}}$
1503	Find the Derivative - d/dt	4t	$4 t$
1504	Find the Derivative - d/dt	-1/((3+t)^2)	$- \frac{1}{{(3 + t)}^{2}}$
1505	Find the Derivative - d/dx	8sin(x)	$8 \sin (x)$
1506	Find the Derivative - d/dx	-2cos(x)	$- 2 \cos (x)$
1507	Find the 2nd Derivative	x^3	$x^{3}$
1508	Evaluate Using L'Hospital's Rule	limit as x approaches 8 of arctan(e^x)	$lim_{x \to 8} \arctan (e^{x})$
1509	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x+x)^(1/x)	$lim_{x \to 0} {(e^{x} + x)}^{\frac{1}{x}}$
1510	Evaluate the Integral	integral of (e^x+e^(-x))/(e^x-e^(-x)) with respect to x	$\int \frac{e^{x} + e^{- x}}{e^{x} - e^{- x}} d x$
1511	Evaluate the Integral	integral of (( natural log of x)^6)/x with respect to x	$\int \frac{\ln^{6} (x)}{x} d x$
1512	Evaluate the Integral	integral of x/2 with respect to x	$\int \frac{x}{2} d x$
1513	Evaluate the Integral	integral from 0 to 1 of 2xe^x with respect to x	$\int_{0}^{1} 2 x e^{x} d x$
1514	Evaluate the Integral	integral of 1/( square root of x^2+100) with respect to x	$\int \frac{1}{\sqrt{x^{2} + 100}} d x$
1515	Evaluate the Integral	integral from 1 to e of natural log of x with respect to x	$\int_{1}^{e} \ln (x) d x$
1516	Evaluate the Integral	integral of 3e^x with respect to x	$\int 3 e^{x} d x$
1517	Evaluate the Integral	integral of x natural log of 3+x with respect to x	$\int x \ln (3 + x) d x$
1518	Find the 2nd Derivative	cos(x^2)	$\cos (x^{2})$
1519	Find the 2nd Derivative	f(x) = square root of x^2+11	$f (x) = \sqrt{x^{2} + 11}$
1520	Find the 2nd Derivative	f(x) = square root of x^2+27	$f (x) = \sqrt{x^{2} + 27}$
1521	Find the 2nd Derivative	y=-2	$y = - 2$
1522	Find the 2nd Derivative	y = square root of x+6	$y = \sqrt{x + 6}$
1523	Find the 2nd Derivative	x(x-4)^3	$x {(x - 4)}^{3}$
1524	Find the 2nd Derivative	f(x)=e^(7x^2+3)	$f (x) = e^{7 x^{2} + 3}$
1525	Evaluate the Limit	limit as x approaches -5 of (x^2-25)/(x+5)	$lim_{x \to - 5} \frac{x^{2} - 25}{x + 5}$
1526	Evaluate the Integral	integral of 1/(4-x^2) with respect to x	$\int \frac{1}{4 - x^{2}} d x$
1527	Evaluate the Integral	integral of 1/( natural log of x) with respect to x	$\int \frac{1}{\ln (x)} d x$
1528	Evaluate the Integral	integral of xcos(4x) with respect to x	$\int x \cos (4 x) d x$
1529	Evaluate the Integral	integral of 1/(x natural log of (x)^2) with respect to x	$\int \frac{1}{x \ln ({(x)}^{2})} d x$
1530	Evaluate the Integral	integral of 1/(1+ square root of x) with respect to x	$\int \frac{1}{1 + \sqrt{x}} d x$
1531	Evaluate the Integral	integral of 1/( cube root of x+ fourth root of x) with respect to x	$\int \frac{1}{\sqrt[3]{x} + \sqrt[4]{x}} d x$
1532	Evaluate the Integral	integral from 0 to 1 of (x^2+2)e^(-x) with respect to x	$\int_{0}^{1} (x^{2} + 2) e^{- x} d x$
1533	Evaluate the Integral	integral of 1/( square root of 2x) with respect to x	$\int \frac{1}{\sqrt{2 x}} d x$
1534	Evaluate the Integral	integral of arctan(2t) with respect to t	$\int \arctan (2 t) d t$
1535	Evaluate the Integral	integral of (xe^(2x))/((2x+1)^2) with respect to x	$\int \frac{x e^{2 x}}{{(2 x + 1)}^{2}} d x$
1536	Evaluate the Integral	integral of (x^3)/3 with respect to x	$\int \frac{x^{3}}{3} d x$
1537	Evaluate the Integral	integral of (x^3-7)/x with respect to x	$\int \frac{x^{3} - 7}{x} d x$
1538	Evaluate the Integral	integral of cos(8x) with respect to x	$\int \cos (8 x) d x$
1539	Evaluate the Integral	integral of (6+x^2)/x with respect to x	$\int \frac{6 + x^{2}}{x} d x$
1540	Evaluate the Integral	integral of z/(e^z) with respect to z	$\int \frac{z}{e^{z}} d z$
1541	Evaluate the Integral	integral of (2x^2+7x-3)/(x-2) with respect to x	$\int \frac{2 x^{2} + 7 x - 3}{x - 2} d x$
1542	Evaluate the Integral	22 integral from 0 to 1 of x^3 square root of 1-x^2 with respect to x	$22 \int_{0}^{1} x^{3} \sqrt{1 - x^{2}} d x$
1543	Evaluate the Integral	integral of xsin(4x) with respect to x	$\int x \sin (4 x) d x$
1544	Evaluate the Integral	integral of (4-5x)^6 with respect to x	$\int {(4 - 5 x)}^{6} d x$
1545	Evaluate the Integral	integral from 0 to 5 of square root of x^2+25 with respect to x	$\int_{0}^{5} \sqrt{x^{2} + 25} d x$
1546	Evaluate the Integral	integral from 0 to 3 of square root of 5 with respect to x	$\int_{0}^{3} \sqrt{5} d x$
1547	Evaluate the Integral	integral of (sin(x))/(1+cos(x)) with respect to x	$\int \frac{\sin (x)}{1 + \cos (x)} d x$
1548	Evaluate the Integral	integral of square root of 1-x with respect to x	$\int \sqrt{1 - x} d x$
1549	Evaluate the Integral	integral of tan(x)^3sec(x) with respect to x	$\int \tan^{3} (x) \sec (x) d x$
1550	Evaluate the Integral	integral of cot(x)^3 with respect to x	$\int \cot^{3} (x) d x$
1551	Evaluate the Integral	integral from 0 to 1 of (x^2+5)e^(-x) with respect to x	$\int_{0}^{1} (x^{2} + 5) e^{- x} d x$
1552	Evaluate the Integral	integral of e^(2x)(1+e^(2x))^3 with respect to x	$\int e^{2 x} {(1 + e^{2 x})}^{3} d x$
1553	Evaluate the Integral	integral of e^(-x/2) with respect to x	$\int e^{- \frac{x}{2}} d x$
1554	Evaluate the Integral	integral of ( natural log of x)/(x^4) with respect to x	$\int \frac{\ln (x)}{x^{4}} d x$
1555	Evaluate the Integral	integral of ( natural log of 5x)/x with respect to x	$\int \frac{\ln (5 x)}{x} d x$
1556	Evaluate the Integral	integral of x^(4/3) with respect to x	$\int x^{\frac{4}{3}} d x$
1557	Evaluate the Integral	integral of x/( square root of x-3) with respect to x	$\int \frac{x}{\sqrt{x - 3}} d x$
1558	Evaluate the Integral	integral of x^2 square root of x+1 with respect to x	$\int x^{2} \sqrt{x + 1} d x$
1559	Evaluate the Integral	integral of x^2*sin(x) with respect to x	$\int x^{2} \cdot \sin (x) d x$
1560	Evaluate the Integral	integral from -1 to 2 of (x-8\|x\|) with respect to x	$\int_{- 1}^{2} (x - 8 \| x \|) d x$
1561	Find the Derivative - d/d@VAR	f(x)=1/(x^3)	$f (x) = \frac{1}{x^{3}}$
1562	Evaluate the Integral	integral of square root of x-1 with respect to x	$\int \sqrt{x - 1} d x$
1563	Evaluate the Integral	integral of x square root of 4-x with respect to x	$\int x \sqrt{4 - x} d x$
1564	Evaluate the Integral	integral of 1/(1+cos(x)) with respect to x	$\int \frac{1}{1 + \cos (x)} d x$
1565	Evaluate the Integral	integral of (x+4)/( square root of x) with respect to x	$\int \frac{x + 4}{\sqrt{x}} d x$
1566	Evaluate the Integral	integral of -32 with respect to t	$\int - 32 d t$
1567	Evaluate the Integral	integral of 3x^5 with respect to x	$\int 3 x^{5} d x$
1568	Evaluate the Integral	integral of (x^2+10x)cos(x) with respect to x	$\int (x^{2} + 10 x) \cos (x) d x$
1569	Evaluate the Integral	integral of e^t with respect to t	$\int e^{t} d t$
1570	Evaluate the Integral	integral of 4(4x+3)^4 with respect to x	$\int 4 {(4 x + 3)}^{4} d x$
1571	Find the Derivative - d/dx	2sin(2x)	$2 \sin (2 x)$
1572	Evaluate the Integral	integral of x^3sin(x) with respect to x	$\int x^{3} \sin (x) d x$
1573	Evaluate the Integral	integral from 0 to pi of cos(x) with respect to x	$\int_{0}^{π} \cos (x) d x$
1574	Evaluate the Integral	integral of 3x(x^2-3)^7 with respect to x	$\int 3 x {(x^{2} - 3)}^{7} d x$
1575	Evaluate the Integral	integral of te^(-6t) with respect to t	$\int t e^{- 6 t} d t$
1576	Evaluate the Integral	integral of sec(2x)tan(2x) with respect to x	$\int \sec (2 x) \tan (2 x) d x$
1577	Evaluate the Integral	integral of xcos(2x) with respect to x	$\int x \cos (2 x) d x$
1578	Evaluate the Integral	integral from 0 to 1 of e^x with respect to x	$\int_{0}^{1} e^{x} d x$
1579	Evaluate the Integral	integral of x square root of x-7 with respect to x	$\int x \sqrt{x - 7} d x$
1580	Evaluate the Integral	integral from 0 to 1 of x^9(1+x^10)^9 with respect to x	$\int_{0}^{1} x^{9} {(1 + x^{10})}^{9} d x$
1581	Evaluate the Integral	integral of natural log of 5x-4 with respect to x	$\int \ln (5 x - 4) d x$
1582	Evaluate the Integral	integral of (x^3)/( square root of x^2+4) with respect to x	$\int \frac{x^{3}}{\sqrt{x^{2} + 4}} d x$
1583	Evaluate the Integral	integral from 0 to 2 of e^x with respect to x	$\int_{0}^{2} e^{x} d x$
1584	Evaluate the Integral	integral of cos(x/5) with respect to x	$\int \cos (\frac{x}{5}) d x$
1585	Evaluate the Integral	integral from 0 to 1 of b square root of 1-b^2 with respect to b	$\int_{0}^{1} b \sqrt{1 - b^{2}} d b$
1586	Evaluate the Integral	integral from 0 to 1 of xe^(x^2) with respect to x	$\int_{0}^{1} x e^{x^{2}} d x$
1587	Evaluate the Integral	integral of x square root of 1-x with respect to x	$\int x \sqrt{1 - x} d x$
1588	Evaluate the Integral	integral from 0 to 5 of x with respect to x	$\int_{0}^{5} x d x$
1589	Evaluate the Integral	integral from 0 to 3 of 3x with respect to x	$\int_{0}^{3} 3 x d x$
1590	Evaluate the Integral	integral of xe^(6x) with respect to x	$\int x e^{6 x} d x$
1591	Evaluate the Integral	integral from 1 to 5 of x/( square root of 2x-1) with respect to x	$\int_{1}^{5} \frac{x}{\sqrt{2 x - 1}} d x$
1592	Evaluate the Integral	integral of 5/x with respect to x	$\int \frac{5}{x} d x$
1593	Evaluate the Integral	integral from 0 to 4 of x^2 with respect to x	$\int_{0}^{4} x^{2} d x$
1594	Evaluate the Integral	integral from 0 to 3 of \|2x-3\| with respect to x	$\int_{0}^{3} \| 2 x - 3 \| d x$
1595	Evaluate the Integral	integral from 0 to 3 of \|x-1\| with respect to x	$\int_{0}^{3} \| x - 1 \| d x$
1596	Evaluate the Integral	integral from 0 to 2 of 6x^2 with respect to x	$\int_{0}^{2} 6 x^{2} d x$
1597	Evaluate the Integral	integral from 0 to 2 of x(x-3) with respect to x	$\int_{0}^{2} x (x - 3) d x$
1598	Evaluate the Integral	integral from 7 to 8 of x square root of x-7 with respect to x	$\int_{7}^{8} x \sqrt{x - 7} d x$
1599	Evaluate the Integral	integral from 1 to 16 of (x-5)/( square root of x) with respect to x	$\int_{1}^{16} \frac{x - 5}{\sqrt{x}} d x$
1600	Evaluate the Integral	integral of (a+bx^2)/( square root of 3ax+bx^3) with respect to x	$\int \frac{a + b x^{2}}{\sqrt{3 a x + b x^{3}}} d x$