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Popular Calculus Problems

derivative of 12arccot(ax^2)	\frac{d}{dx}(12\arccot(ax^{2}))
integral of sin(2t)	\int\:\sin(2t)dt
integral from 0 to pi/4 of tan^5(x)	\int\:_{0}^{\frac{π}{4}}\tan^{5}(x)dx
integral from 0 to pi of 19sin^2(4x)	\int\:_{0}^{π}19\sin^{2}(4x)dx
integral of t+4	\int\:t+4dt
tangent of f(x)=sin(sin(x)),\at x=3pi,0	tangent\:f(x)=\sin(\sin(x)),\at\:x=3π,0
derivative of a^x	derivative\:a^{x}
(3x^2y^2+y)dx+(2x^3y+x)dy=0	(3x^{2}y^{2}+y)dx+(2x^{3}y+x)dy=0
area y=e^x,y=e^{-4x},x=ln(3)	area\:y=e^{x},y=e^{-4x},x=\ln(3)
integral of xsqrt(x+4)	\int\:x\sqrt{x+4}dx
integral from 0 to pi/6 of cos^3(x)	\int\:_{0}^{\frac{π}{6}}\cos^{3}(x)dx
integral of (5x^4+3x^2+2x)	\int\:(5x^{4}+3x^{2}+2x)dx
integral of 16xln(7x)	\int\:16x\ln(7x)dx
integral from 0 to pi/2 of 11sin^2(2x)	\int\:_{0}^{\frac{π}{2}}11\sin^{2}(2x)dx
integral of (sqrt(a^2-x^2))/x	\int\:\frac{\sqrt{a^{2}-x^{2}}}{x}dx
xy^'+2y=4x^2	xy^{\prime\:}+2y=4x^{2}
derivative of (-e^{1/x}/(x^2))	\frac{d}{dx}(\frac{-e^{\frac{1}{x}}}{x^{2}})
y^{''}+5y^'+6y=2x	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=2x
derivative of x^3*sin^2(5x)	\frac{d}{dx}(x^{3}\cdot\:\sin^{2}(5x))
limit as x approaches 1 of 1/(sqrt(1-x))	\lim\:_{x\to\:1}(\frac{1}{\sqrt{1-x}})
integral of (x+1/x)^2(x-1/x)^2-x+1/x	\int\:(x+\frac{1}{x})^{2}(x-\frac{1}{x})^{2}-x+\frac{1}{x}dx
(\partial)/(\partial y)(arctan(xsqrt(t)))	\frac{\partial\:}{\partial\:y}(\arctan(x\sqrt{t}))
(\partial)/(\partial x)((sin(x))/(sin(y)))	\frac{\partial\:}{\partial\:x}(\frac{\sin(x)}{\sin(y)})
integral from 0 to 4 of (4-x)sqrt(x)	\int\:_{0}^{4}(4-x)\sqrt{x}dx
integral from 0 to 4 of pi(1/(x+3))^2	\int\:_{0}^{4}π(\frac{1}{x+3})^{2}dx
integral from 0 to x of t^2cos(t)	\int\:_{0}^{x}t^{2}\cos(t)dt
integral of 3x-x^2	\int\:3x-x^{2}dx
derivative of (2x-sqrt(x))(5x+2)	derivative\:(2x-\sqrt{x})(5x+2)
tangent of f(x)=x^3-2x+1,(2,5)	tangent\:f(x)=x^{3}-2x+1,(2,5)
d/(dt)(sqrt(3t))	\frac{d}{dt}(\sqrt{3t})
simplify 16ln(x^2)-x^2	simplify\:16\ln(x^{2})-x^{2}
(\partial)/(\partial x)(e^{4xy}*4y)	\frac{\partial\:}{\partial\:x}(e^{4xy}\cdot\:4y)
derivative of (x^n/n)	\frac{d}{dx}(\frac{x^{n}}{n})
derivative of e^{-x}arcsin(4e^x)	\frac{d}{dx}(e^{-x}\arcsin(4e^{x}))
derivative of e^{xcos(x})	\frac{d}{dx}(e^{x\cos(x)})
y^'+y^{1/2}=0	y^{\prime\:}+y^{\frac{1}{2}}=0
(sin^2(t))^'	(\sin^{2}(t))^{\prime\:}
derivative of-18sin(3x)	\frac{d}{dx}(-18\sin(3x))
limit as x approaches 0+of x^4	\lim\:_{x\to\:0+}(x^{4})
limit as x approaches-3 of (x+1)/(x+3)	\lim\:_{x\to\:-3}(\frac{x+1}{x+3})
slope of (19,3),(20,3)	slope\:(19,3),(20,3)
integral of (x-2/x)^2	\int\:(x-\frac{2}{x})^{2}dx
derivative of 14sin(x)	\frac{d}{dx}(14\sin(x))
limit as x approaches-2 of (x^3)/(x-2)	\lim\:_{x\to\:-2}(\frac{x^{3}}{x-2})
integral of 4y^3	\int\:4y^{3}dy
derivative of f(x)=2x-1	derivative\:f(x)=2x-1
integral of 12e^{3x}	\int\:12e^{3x}dx
integral of (1-t)(2+t^2)	\int\:(1-t)(2+t^{2})dt
(d^2)/(dx^2)(cot(2x)+3x^2)	\frac{d^{2}}{dx^{2}}(\cot(2x)+3x^{2})
derivative of log_{2}(2x)	\frac{d}{dx}(\log_{2}(2x))
derivative of arccot(x/2)	\frac{d}{dx}(\arccot(\frac{x}{2}))
tangent of f(x)=7-x^2	tangent\:f(x)=7-x^{2}
integral from 0 to 20 of 1	\int\:_{0}^{20}1
integral of 5x^2sin(pix)	\int\:5x^{2}\sin(πx)dx
derivative of ln\|x+1\|	\frac{d}{dx}(\ln\left\|x+1\right\|)
derivative of sqrt(x^2-\sqrt{2x)}	\frac{d}{dx}(\sqrt{x^{2}-\sqrt{2x}})
derivative of (x-4/(3x-x^2))	\frac{d}{dx}(\frac{x-4}{3x-x^{2}})
integral of sqrt(2+2cos(x))	\int\:\sqrt{2+2\cos(x)}dx
integral of (u^2)/(1+u^2)	\int\:\frac{u^{2}}{1+u^{2}}du
area y=2x^2,y=8x^2,5x+y=3	area\:y=2x^{2},y=8x^{2},5x+y=3
derivative of 2e^x+xe^x	\frac{d}{dx}(2e^{x}+xe^{x})
tangent of f(x)=8+5x^2-2x^3,(2,12)	tangent\:f(x)=8+5x^{2}-2x^{3},(2,12)
integral from 7 to 9 of 7/((x-8)^{10)}	\int\:_{7}^{9}\frac{7}{(x-8)^{10}}dx
integral of ((x^2-x+42))/(x^3+7x)	\int\:\frac{(x^{2}-x+42)}{x^{3}+7x}dx
derivative of-(x+1(x-1)^2)	\frac{d}{dx}(-(x+1)(x-1)^{2})
derivative of f(x)=((x+3)/(x-3))^5	derivative\:f(x)=(\frac{x+3}{x-3})^{5}
integral of (x+1/(x^3))	\int\:(x+\frac{1}{x^{3}})dx
sum from n=1 to infinity of 1/2 (0.3)^n	\sum\:_{n=1}^{\infty\:}\frac{1}{2}(0.3)^{n}
tangent of f(x)= 3/x ,\at x=-5	tangent\:f(x)=\frac{3}{x},\at\:x=-5
inverse oflaplace ((s^2))/(s^2+1)	inverselaplace\:\frac{(s^{2})}{s^{2}+1}
integral of (1-x^2)/(1-2x)	\int\:\frac{1-x^{2}}{1-2x}dx
integral from 1/2 to 3 of 16xln(2x)	\int\:_{\frac{1}{2}}^{3}16x\ln(2x)dx
(\partial)/(\partial x)(ln(r/(ro)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{r}{ro}))
(x^2+y)(dy)/(dx)-y-3x^2=2y	(x^{2}+y)\frac{dy}{dx}-y-3x^{2}=2y
integral of sqrt(x+13)	\int\:\sqrt{x+13}dx
limit as x approaches 2 of (5x+2)/(x-2)	\lim\:_{x\to\:2}(\frac{5x+2}{x-2})
derivative of e^{jx}	\frac{d}{dx}(e^{jx})
y^'=sqrt(y^2-9)	y^{\prime\:}=\sqrt{y^{2}-9}
taylor 1/(x^2+1)	taylor\:\frac{1}{x^{2}+1}
integral of cos(x)(8+4sin^2(x))	\int\:\cos(x)(8+4\sin^{2}(x))dx
derivative of y=cos(x^3)	derivative\:y=\cos(x^{3})
limit as x approaches 5 of (x^2-3x-10)/(x-5)	\lim\:_{x\to\:5}(\frac{x^{2}-3x-10}{x-5})
derivative of (7x-8^5)	\frac{d}{dx}((7x-8)^{5})
(\partial)/(\partial x)(ln(2ye^{xy}))	\frac{\partial\:}{\partial\:x}(\ln(2ye^{xy}))
derivative of (sqrt(x+1)/(sqrt(x-1)))	\frac{d}{dx}(\frac{\sqrt{x+1}}{\sqrt{x-1}})
derivative of x^{x^x}	\frac{d}{dx}(x^{x^{x}})
limit as x approaches infinity of (2^{-x}-2^x)/(2^{-x)+2^x}	\lim\:_{x\to\:\infty\:}(\frac{2^{-x}-2^{x}}{2^{-x}+2^{x}})
integral of (2x)/(3x^2-4)	\int\:\frac{2x}{3x^{2}-4}dx
derivative of 3/(5+x^2)	derivative\:\frac{3}{5+x^{2}}
sum from n=1 to infinity of ((-2)/3)^n	\sum\:_{n=1}^{\infty\:}(\frac{-2}{3})^{n}
integral of 9xln(x)	\int\:9x\ln(x)dx
limit as x approaches-2 of 4^xcos(pix)	\lim\:_{x\to\:-2}(4^{x}\cos(πx))
taylor e^{3x^3}	taylor\:e^{3x^{3}}
derivative of y=sqrt(x)(x-8)	derivative\:y=\sqrt{x}(x-8)
derivative of 2^{3x+1}	derivative\:2^{3x+1}
d/(d{r)}(({r})/(sqrt({r)^2+1)})	\frac{d}{d{r}}(\frac{{r}}{\sqrt{{r}^{2}+1}})
normal of f(x)=x*5^x,\at x=1	normal\:f(x)=x\cdot\:5^{x},\at\:x=1
integral of sqrt(1-x)	\int\:\sqrt{1-x}dx
y^{''}-3y^'+2y=2e^3t	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=2e^{3}t
limit as x approaches infinity of 8/x	\lim\:_{x\to\:\infty\:}(\frac{8}{x})

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