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Mathematics
Mathematics
Problem
Evaluate the following integrals step by step and hence obtain the antiderivative of the complete expression. (i) Find
∫
5
e
3
x
d
x
.
\int 5e^{3x}\,dx.
∫
5
e
3
x
d
x
.
(ii) Find
∫
−
4
sec
2
x
d
x
.
\int -4\sec^2 x\,dx.
∫
−
4
sec
2
x
d
x
.
(iii) Hence determine
∫
(
5
e
3
x
−
4
sec
2
x
)
d
x
.
\int \bigl(5e^{3x}-4\sec^2 x\bigr)\,dx.
∫
(
5
e
3
x
−
4
sec
2
x
)
d
x
.
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