What is the integral of x^2cos(x^3+10) ?

The integral of x^2cos(x^3+10) is 1/3 sin(x^3+10)+C

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integral of x^2cos(x^3+10)

\int x^{2} cos (x^{3} + 10) d x

\frac{1}{3} sin (x^{3} + 10) + C

Solution steps

\int x^{2} cos (x^{3} + 10) d x

Apply u-substitution

: \int \frac{u cos ( u ^{\frac{3}{2}} + 10 )}{2 x} d u

= \int \frac{cos ( u + 10 )}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int cos (u + 10) d u

Apply u-substitution

: \int cos (v) d v

= \frac{1}{3} \cdot \int cos (v) d v

Use the common integral:

\int cos (v) d v = sin (v)

= \frac{1}{3} sin (v)

Substitute back

= \frac{1}{3} sin (x^{3} + 10)

Add a constant to the solution

= \frac{1}{3} sin (x^{3} + 10) + C

ln (1 - x)

\int \frac{y ^{5}}{1 - y ^{4}} d y

\frac{\partial}{\partial t} (\frac{s}{t})

x \to 4 lim (2 x^{4} - x^{2} - 8 x)

What is the integral of x^2cos(x^3+10) ?
The integral of x^2cos(x^3+10) is 1/3 sin(x^3+10)+C