What is the integral of (e^x(1+x))/(cos^2(xe^x)) ?

The integral of (e^x(1+x))/(cos^2(xe^x)) is tan(xe^x)+C

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integral of (e^x(1+x))/(cos^2(xe^x))

\int \frac{e ^{x} ( 1 + x )}{cos ^{2} ( x e ^{x} )} d x

tan (x e^{x}) + C

Solution steps

\int \frac{e ^{x} ( 1 + x )}{cos ^{2} ( x e ^{x} )} d x

Apply u-substitution

: \int sec^{2} (u) d u

= \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= tan (u)

Substitute back

u = x e^{x}

= tan (x e^{x})

Add a constant to the solution

= tan (x e^{x}) + C

\frac{d}{d x} (\frac{x}{8} - \frac{8}{x})

f (x) = sin (x), (0, 0)

(1.7) (10.8)

\int_{1}^{10} \frac{33}{x ^{3}} d x

\frac{1}{s ^{2} + 2 \cdot 0.5 \cdot 1 s + 1}

What is the integral of (e^x(1+x))/(cos^2(xe^x)) ?
The integral of (e^x(1+x))/(cos^2(xe^x)) is tan(xe^x)+C